Emergency services were quickly sent to the scene, in Edgbaston, where the woman was pronounced dead.

Detectives immediately launched an investigation into the circumstances of the woman’s death and at just after 7pm last night, a 39-year-old man was arrested on suspicion of her murder.

Police outside Century Tower in Dollery Drive, off the Bristol Road, Edgbaston, where a woman's body was found

A forensic post mortem examination and formal identification will be carried out later today. The victim has yet to be officially identified.

One tower block resident, who wished to remain anonymous, said: “I heard a commotion on the night, early morning. I didn’t take much notice. When it quietened down, I went to sleep and the morning the police came knocking at the door.”

Another resident, Patrick Morgan, a 36-year-old labourer, said: “There was a lot of shouting outside.

“I looked out the window and went back to bed. When I woke up at 5am, I saw five police cars and two ambulances.” Hotel worker Michael Winnal, 25, who also lives in the block, said: “Yesterday, I came outside and there was a lot of police everywhere at the exits and entrances asking for everyone’s address and date of birth.

“I spoke to someone on the way to the shops and they said it was a lady in her 50s.

“It’s bad, nothing like this had happened before and I’ve been here for three to four years.”

Det Insp Ian Iliffe is leading the murder investigation. He said: “We urge anyone who has information to help our investigation to come forward at the earliest opportunity.

“At this stage it is still unclear when the lady may have died and we await the results of a post mortem later to determine the circumstances.